Maximum ball-screw speed depends on system design, lubrication, and thermal conditions [S6].
The allowable command speed must satisfy three independent limits: the shaft critical speed, the DN-based permissible rotational speed, and the lower maximum speed assigned to the nut [S2][S3].
Critical Speed Is a Resonance Boundary, Not a Speed Rating
Critical speed is the first rotational speed at which the screw shaft resonates, and it corresponds to the first-order natural frequency of the rotating shaft [S1][S7]. As the screw rotates through its first bending mode, the shaft begins to whip in the same general manner as a jump rope [S7].
The permissible rotational speed must be obtained from the critical speed of the screw shaft and its DN value [S2]. This matters because critical speed alone describes a structural resonance boundary, while DN supplies the drive-speed context needed to establish a permissible operating speed [S1][S2].
For fixed ball-screw assemblies, the operating limit cannot be separated from the end-support arrangement because bearing support changes the critical speed [S5]. A screw with fixed-fixed support has a different speed boundary from an otherwise comparable screw with simple-simple or fixed-free support [S5].
DN Value Defines the Permissible Drive Speed
The DN value is the factor used with critical speed to determine the permissible rotational speed of the ball screw [S2]. Critical speed defines where shaft resonance begins, whereas the DN-based result establishes how far below that boundary the selected screw may be driven [S1][S2].
The example does not establish a universal rpm-to-diameter equation, but it demonstrates why a large-diameter screw should not be assigned the same speed envelope as a miniature screw.
The three speed concepts should remain separate in the specification: critical speed is the shaft resonance boundary, driving speed is based on DN, and maximum speed is the upper operational limit of the complete ball-screw system [S1][S4][S6]. Maximum speed depends on system design, lubrication, and thermal conditions, not on shaft resonance alone [S6].
Compare the Three Governing Speed Limits
The three governing limits answer different engineering questions: critical speed asks whether the shaft is dynamically stable, the DN-based speed asks what drive speed is permissible for the selected screw, and the nut limit asks whether the ball nut can physically tolerate the commanded rpm [S2][S3][S6].
The final operating speed is therefore the lowest applicable value, not the average or the most favorable one. If a nut is rated for 3,000 rpm and the DN-based shaft limit is 2,400 rpm, the assembly should be limited to 2,400 rpm before any additional application margin is applied. Thomson likewise states that the screw and nut have individual maximum rpm ratings that should not be exceeded [S3].
Support Length and End Bearings Change the Result
A critical-speed calculation requires the required rpm, the maximum unsupported length between bearing supports, and the end-support configuration [S5]. The standard support categories used for this comparison are fixed-free, simple-simple, fixed-simple, and fixed-fixed [S5].
The chart method locates the intersection of the required rpm and unsupported length, then compares that point with the screw-diameter curve [S5]. This is more defensible than selecting a screw from diameter and lead alone, because a longer unsupported span lowers the speed at which the shaft develops resonant whip.
The original guidance behind the chart recommends operating at no more than 80% of the critical-speed limit to accommodate misalignment or imperfect screw straightness [S5]. That recommendation provides a practical margin below the theoretical resonance boundary, but it does not override the DN-based permissible speed or the nut and system limits [S2][S3][S6].
Ball-screw selection is also constrained by geometry and stiffness, including the relationship between screw diameter and lead. The ball screw diameter-to-lead ratio for rigidity comparison explains why choosing a larger lead to reach higher linear speed can reduce axial rigidity.
Operating Below Resonance Still Leaves Thermal Limits
Maximum system speed is governed by design, lubrication, and thermal conditions, so a shaft that remains below critical speed can still overheat if grease, lubrication method, travel duty cycle, or heat removal is inadequate [S6]. Resonant vibration is one failure boundary, not the only one.
The nut requires its own rating check because a ball-screw assembly has maximum operating speeds for both the screw and the nut, and neither should be exceeded [S3]. For a general description of the mechanical element involved, see ball screw; critical-speed calculations still require the exact shaft geometry and support conditions.
Ball size can be used as an initial screening parameter, but maximum speed depends on the ball-screw system's design, lubrication, and thermal conditions [S6]. The selected component’s manufacturer must provide the applicable rating because nut construction, shaft diameter, lead, and mounting can materially change the result [S2][S3][S6].
Specification Rules for a Defensible Speed Limit
A defensible speed specification requires the maximum operating rpm, DN value, screw diameter, maximum unsupported length, and end-support arrangement to be identified before the assembly is released [S2][S5]. These inputs permit the critical-speed calculation to be checked against the DN-based permissible speed and the separate nut rating [S2][S3].
Three acceptance rules should then be applied. First, the selected rpm must remain below the shaft resonance boundary. Second, it must not exceed the DN-based permissible rotational speed. Third, it must not exceed the lower nut or complete-system maximum speed [S2][S3][S6].
For rolled screws, the chart guidance uses the smallest root diameter of standard screws within each nominal size range and stops at the maximum ball-nut rotational speed; neither the diameter curve nor shaft length overrides the nut limit [S5]. Where the operating point enters a dashed portion of a curve, manufacturer consultation is required [S5].
Before commissioning, verify that the support span matches the calculation, check that the drive cannot command above the approved rpm, and confirm that the lubrication method can manage the heat generated at the selected speed [S5][S6]. The most useful trackable document is the manufacturer’s speed table, not a generic rpm value copied from another screw size or mounting arrangement.